Virtual displacement and D'Alembert's principle

Click For Summary
Virtual displacement is a crucial concept in Lagrangian mechanics, representing small spatial changes in a system without any time displacement. It plays a significant role in the application of D'Alembert's principle, which is foundational for deriving the Lagrangian equation. The least action principle states that the actual path taken by a particle is one where the action remains stationary, meaning that virtual displacements do not affect the action. This principle helps in simplifying complex mechanical systems by focusing on energy conservation and motion paths. Understanding virtual displacement enhances the analysis of dynamic systems in classical physics.
manimaran1605
Messages
60
Reaction score
0
While deriving lagrangian equation using D'Alembert's principle, in Goldstien, they defined a variable called "virtual displacement". Why do we need a concept called virtual displacement? What is its signigicance in classical physics?
 
Physics news on Phys.org
Hi,

You can read in wikipedia about it:

http://en.wikipedia.org/wiki/Virtual_displacement

I am not an expert on this matter but from what I have seen, virtual displacements are small spatial displacements r_{i} (with no time displacement) over the path of motion and are used in Lagrangian mechanics.

The least action principle is part of Lagrangian mechanics and states that particles follow a path whose action is stationary, which means that any "small" virtual displacements does not change the action.

You can also read about the least action principle in wikipedia:

http://en.wikipedia.org/wiki/Principle_of_least_action



Sergio
 
  • Like
Likes 1 person
Thread 'What is the pressure of trapped air inside this tube?'

Thread 'What is the pressure of trapped air inside this tube?'

As you can see from the picture, i have an uneven U-shaped tube, sealed at the short end. I fill the tube with water and i seal it. So the short side is filled with water and the long side ends up containg water and trapped air. Now the tube is sealed on both sides and i turn it in such a way that the traped air moves at the short side. Are my claims about pressure in senarios A & B correct? What is the pressure for all points in senario C? (My question is basically coming from watching...
View full post »

Similar threads

Undergrad Virtual displacement is not consistent with constraints
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Requirement of Holonomic Constraints for Deriving Lagrange Equations
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Extending Hamilton's principle to systems with constraints
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Study Lagrangian Mechanics: D'Alembert's Principle
  • · Replies 2 ·
Replies
2
Views
1K
Why is D'Alembert's Principle stated in terms of virtual displacements?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate An ab initio Hilbert space formulation of Lagrangian mechanics
  • · Replies 10 ·
Replies
10
Views
2K
Graduate The Lagrange–d'Alembert principle for rigid bodies
  • · Replies 1 ·
Replies
1
Views
1K
Why is Hamilton's Principle assumed to be valid for non-holonomic systems?
  • · Replies 25 ·
Replies
25
Views
3K
What Is Virtual Displacement in the D'Alembert Principle?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Physical interpretation of virtual displacement
  • · Replies 12 ·
Replies
12
Views
4K